Whether someone has done a user defined version of Blinn-Phong (not Blinn and not Phong separately) reflection model in the node editor?
Q. I want to know is there any possibility to define Blinn-Phong reflection model as a user defined reflection model?

A. Yes

Q.If yes, should I use Blender "Node Editor" to define a new material?

A. Yes

Q. Has anyone done this before?

A. Yes, quite so.

I will try not to write a 2718 page treatise here.  Cycles render engine is designed as a photo realistic (PR) physics based renderer. Blender render is a respectable renderer different than cycles.  I am trying to give you some terms for further research.  Your public library probably has electronic titles on Cycles and there is the general internet and there are just a few video tutorials on video websites.

If we look at the node system for Cycles we are delivered fragments with geometric surface normal information, camera information and more.  Vector operations resulting in scalars such as dot product are available and are quite relevant to shading.  So you have the freedom to write original or not so original shaders.  Your results can be physics based or artistically styled.  Many relevant math functions are available such as sine, cosine, modulus. Your image is as unlimited as your creativity.

Know that dot product and vector product are your BFF when shading.  Just remember to get some sleep once in a while.  Try to take breaks every 8 hours of writing material nodes.